4 citations · 17 across the 48 of their papers we have counts for
48 papers
On some conjectural series containing harmonic numbers of 3-order
Chuanan Wei, Ce Xu
Harmonic numbers are important in a lot of branches of number theory. By means of the derivative operator, the integral operator, and several summation and transformation formulas…
On some conjectural series containing binomial coefficients and harmonic numbers
Chuanan Wei
Binomial coefficients and harmonic numbers are important in many branches of number theory. With the help of the operator method and several summation and transformation formulas f…
On some conjectures of Z.-W. Sun involving harmonic numbers
Chuanan Wei
Harmonic numbers are significant in various branches of number theory. With the help of the digamma function, we prove ten conjectural series of Z.-W. Sun involving harmonic number…
Some fast convergent series for the mathematical constants and
Chuanan Wei
Recently, Sun [preprint, arXiv: 2210.07238v7] proposed two conjectural series for the mathematical constant and two conjectural series for the mathematical constant .…
On a conjectural series of Sun for the mathematical constant
Chuanan Wei
Series expansions for the mathematical constant are rare in the history. With the help of the operator method and a hypergeometric transformation, we prove a surprising conj…
Some multidimensional Rogers--Ramanujan type identities
Chuanan Wei, Yuanbo Yu, Guozhu Ruan
With the help of the contour integral method, we derive a parametric reduction formula that transforms a double series into a single series. This formula recovers two results of Un…
On two conjectural series for and their -analogues
Chuanan Wei
In terms of the operator method, we prove two conjectural series for of Sun involving harmonic numbers of order two. Furthermore, we also give -analogues of six -formulas…
Double series for and their -analogues
Chuanan Wei, Guozhu Ruan
With the help of the partial derivative operator and several summation formulas for hypergeometric series, we find three double series for . In terms of the operator just stated…
Some q-Supercongruences for the truncated q-trinomial coefficients
Chuanan Wei
In 1987, Andrews and Baxter introduced six kinds of -trinomial coefficients in exploring the solution of a model in statistical mechanics. In this paper, we give some -superc…
-Supercongruences from Gasper and Rahman's summation formula
Chuanan Wei
In 2017, He [Proc. Amer. Math. Soc. 145 (2017), 501--508] established two spuercongruences on truncated hypergeometric series and further proposed two related conjectures. Subseque…
New -supercongruences arising from a summation of basic hypergeometric series
Chuanan Wei, Chun Li
With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime…
-Supercongruences from Jackson's summation and Watson's transformation
Chuanan Wei
-Supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some -supercongruences modulo the…
-Supercongruences from the -Saalschütz identity
Chuanan Wei, Yudong Liu, Xiaoxia Wang
In terms of the -Saalschütz identity and the Chinese remainder theorem for coprime polynomials, we establish some -supercongruences modulo the third power of a cyclotomic pol…
-Supercongruences with parameters
Chuanan Wei
In terms of the creative microscoping method recently introduced by Guo and Zudilin [Adv. Math. 346 (2019), 329--358], we find a -supercongruence with four parameters modulo $Φ_…
A further -analogue of Van Hamme's (H.2) supercongruence for
Chuanan Wei
Several years ago, Long and Ramakrishna [Adv. Math. 290 (2016), 773--808] extended Van Hamme's (H.2) supercongruence to the modulus case. Recently, Guo [Int. J. Number Theory…
On the Askey--Wilson type integrals
Chuanan Wei
The Askey--Wilson integral is very important in the theory of orthogonal polynomials. Liu's integral is a generalization of the Askey--Wilson integral with many parameters. With th…
Several transformation formulas involving bilateral basic hypergeometric series
Chuanan Wei, Tong Yu
In terms of the analytic continuation method, we prove three transformation formulas involving bilateral basic hypergeometric series. One of them is equivalent to Jouhet's result i…
Transformation and summation formulas for basic hypergeometric series associated with the circumference ratio
Chuanan Wei
In terms of the difference operators, we establish several curious transformation and summation formulas for basic hypergeometric series. When the parameters are specified, they pr…
The united proofs for three -extensions of Dougall's summation formula
Chuanan Wei
In terms of the analytic continuation method, we give the united proofs for three -extensions of Dougall's summation formula. Some related results are also discussed in…
q-Analogues of several -formulas
Chuanan Wei
According to the -series method, a short proof for Hou and Sun's identity, which is the -analogue of a known -formula, is offered. Furthermore, -analogues of several ot…
Summation formulas involving harmonic numbers with even or odd indexes
Chuanan Wei, Dianxuan Gong, Lily Li Liu
By means of the derivative operator and Chu-Vandermonde convolution, four families of summation formulas involving harmonic numbers with even or odd indexes are established.
Recursion formulas of q-Appell functions
Xiaoxia Wang, Wei Chuanan
Recently, Opps, Saad and Srivastava gave the recursion formulas of Appell's function F2. The first author of this paper then established the recursion formulas for Appell functions…
Partial theta function identities from Wang and Ma's conjecture
Chuanan Wei
Recently, Wang and Ma propose a conjecture associated with the possible generalization of Andrews-Warnaar identities. It is confirmed in this paper. As the applications of this con…
Summation formulas for Fox-Wright function
Chuanan Wei, Lily Li Liu, Dianxuan Gong
By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric seri…